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reformatted link (link is not about alternating group)
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YCor
YCor
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Hermez and Salinier, Rational trinomials with the alternatingRational trinomials with the alternating group as Galois group as Galois group, Journal of Number Theory, Volume 90, Issue 1, September 2001, Pages 113-129 has the abstract,

For any integer $n\ge7$, we show how to explicitly build an infinite number of rational trinomals of degree $n$ whose Galois group over $\bf Q$ is isomorphic to $A_n$.

Hermez and Salinier, Rational trinomials with the alternating group as Galois group, Journal of Number Theory, Volume 90, Issue 1, September 2001, Pages 113-129 has the abstract,

For any integer $n\ge7$, we show how to explicitly build an infinite number of rational trinomals of degree $n$ whose Galois group over $\bf Q$ is isomorphic to $A_n$.

Hermez and Salinier, Rational trinomials with the alternating group as Galois group, Journal of Number Theory, Volume 90, Issue 1, September 2001, Pages 113-129 has the abstract,

For any integer $n\ge7$, we show how to explicitly build an infinite number of rational trinomals of degree $n$ whose Galois group over $\bf Q$ is isomorphic to $A_n$.

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Gerry Myerson
Gerry Myerson
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Hermez and Salinier, Rational trinomials with the alternating group as Galois group, Journal of Number Theory, Volume 90, Issue 1, September 2001, Pages 113-129 has the abstract,

For any integer $n\ge7$, we show how to explicitly build an infinite number of rational trinomals of degree $n$ whose Galois group over $\bf Q$ is isomorphic to $A_n$.